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Mirrors > Home > ILE Home > Th. List > 0ss | Unicode version |
Description: The null set is a subset of any class. Part of Exercise 1 of [TakeutiZaring] p. 22. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
0ss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3337 | . . 3 | |
2 | 1 | pm2.21i 620 | . 2 |
3 | 2 | ssriv 3071 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 wss 3041 c0 3333 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-dif 3043 df-in 3047 df-ss 3054 df-nul 3334 |
This theorem is referenced by: ss0b 3372 ssdifeq0 3415 sssnr 3650 ssprr 3653 uni0 3733 int0el 3771 0disj 3896 disjx0 3898 tr0 4007 0elpw 4058 exmidsssn 4095 fr0 4243 elnn 4489 rel0 4634 0ima 4869 fun0 5151 f0 5283 oaword1 6335 0domg 6699 nnnninf 6991 exmidfodomrlemim 7025 sum0 11112 ennnfonelemj0 11825 ennnfonelemkh 11836 0opn 12084 baspartn 12128 0cld 12192 ntr0 12214 bdeq0 12961 bj-omtrans 13050 el2oss1o 13084 nninfsellemsuc 13104 |
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